In this paper, we propose a model-based machine-learning approach for dual-polarization systems by parameterizing the split-step Fourier method for the Manakov-PMD equation. The resulting method combines hardware-friendly time-domain nonlinearity mitigation via the recently proposed learned digital backpropagation (LDBP) with distributed compensation of polarization-mode dispersion (PMD). We refer to the resulting approach as LDBP-PMD. We train LDBP-PMD on multiple PMD realizations and show that it converges within 1% of its peak dB performance after 428 training iterations on average, yielding a peak effective signal-to-noise ratio of only 0.30 dB below the PMD-free case. Similar to state-of-the-art lumped PMD compensation algorithms in practical systems, our approach does not assume any knowledge about the particular PMD realization along the link, nor any knowledge about the total accumulated PMD. This is a significant improvement compared to prior work on distributed PMD compensation, where knowledge about the accumulated PMD is typically assumed. We also compare different parameterization choices in terms of performance, complexity, and convergence behavior. Lastly, we demonstrate that the learned models can be successfully retrained after an abrupt change of the PMD realization along the fiber.

More generally, one may regard the entire communication system design as an end-to-end reconstruction task and jointly optimize transmitter and receiver NNs [1]. Both traditional [2-4] and end-to-end learning [5-7] have received considerable attention for optical fiber systems. However, the reliance on NNs as universal (but sometimes poorly understood) function approximators makes it difficult to incorporate existing domain knowledge or interpret the obtained solutions. Rather than relying on NNs, a different approach is to start from an existing model and parameterize it. For fiberoptic systems, this can be done for example by considering the split-step method (SSM) for numerically solving the nonlinear Schr odinger equation (NLSE).